Subgroups — C₁₃×C₁₇×#4223 #49136142

Order 36244.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×#4223	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×#4223	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇×D₄₁	C₂×C₁₃	1	1	yes	characteristic
6	C₁₃×D₄₁	C₂×C₁₇	1	1	yes	characteristic
7	C₄×C₁₃×C₁₇	—	41	1	no	maximal, Hall
8	C₁₇×C₄₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₄₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃×C₁₇	—	41	1	no	—
11	C₁₃×C₁₇	#4223	1	1	yes	characteristic, direct product factor, Hall
12	#4223	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	D₄₁	C₂×C₁₃×C₁₇	1	1	yes	characteristic
14	C₄×C₁₇	—	41	1	no	Hall
15	C₄×C₁₃	—	41	1	no	Hall
16	C₄₁	C₄×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₇	—	41	1	no	—
18	C₂×C₁₃	—	41	1	no	—
19	C₁₇	C₁₃×#4223	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₃	C₁₇×#4223	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	41	1	no	Sylow
22	C₂	—	41	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.